Paramagnetism in Pb(Zr,Ti)O₃ nanotube arrays at low temperatures

The nano-ferroelectrics community has taken a keen interest over the past 65 years in achieving the toroidal (circular) ordering of electric domains. Understanding the behavior of vortex ferroelectric domain states remains an unresolved issue because electric polarization density interactions contribute significantly to large extrinsic effects if the strain, charge and size are not tightly controlled. Here, we present an experimental clue to toroidal ordering at low temperatures, that is, the paramagnetism in highly-ordered arrays of ferroelectric Pb(Zr,Ti)O₃ nanotubes composed of nanometer-sized perovskite crystallites. The critical temperature for the phase transition from a normal ferroelectric polar state to toroidal ordering is 70 K.